Extreme value theory for suprema of random variables with regularly varying tail probabilities

Consider a stationary sequence Xj=supiciZj-i,j[set membership, variant]I, where {ci} is a sequence of con {Zi} a sequence of i.i.d. random variables with regularly varying tail probabilities. For suitable normalizing functions [upsilon]1, [upsilon]2,..., the limit form of the two dimensional point process with points (j/n,[upsilon]-1n(Xj)),j[set membership, variant]I, is derived. The implications of the convergence are briefly discussed, while the distribution of the joint exceedances of high levels by {Xj} is explicitly obtained as a corollary.